Design and fabrication of off-axis meta-lens with large focal depth

Ding Ji-Fei; Liu Wen-Bing; Li Han-Hui; Luo Yi; Xie Chen-Kai; Huang Li-Rong

doi:10.7498/aps.70.20202235

Abstract

A kind of off-axis meta-lens with large focal depth based on a single-layer metasurface is designed and fabricated. Our proposed off-axis focus is realized by combining the two functions of deflection and focus through phase superposition method, and the focal depth can be increased by optimizing the input aperture and off-axis deflection angle. Three-dimensional finite difference time domain (FDTD) method is used for numerical simulation to construct the off-axis meta-lens, then the off-axis meta-lens is fabricated and its focus performance is tested in a microwave anechoic chamber.Experimental results indicate that at the designed electromagnetic wave frequency (9 GHz), the measured off-axis deflection angle is 27.5° and the focal length is 335.4 mm, which agree with the designed values of 30° and 350 mm. The measured full-wave half-maximum (FWHM) at the focal point is 48.2 mm, however, the simulated FWHM is 40.2 mm, which means that the imaging quality of the measured focus spot is slightly worse than the simulated one. This is mainly due to the fact that the actual parameters of the fabricated meta-lens are inconsistent with simulated parameters. In addition, during the measurement, the large sampling interval in the x- direction also leads to experimental errors.The focusing efficiency of the off-axis meta-lens at the working frequency of 9 GHz is calculated to be 16.9%. The main reason for the low focusing efficiency is that the plasmonic metasurface works in the transmission mode, which can manipulate only the cross-polarized component of the incident wave, and the maximum efficiency will not exceed 25%. Moreover, the focal depths at 8 GHz, 9 GHz and 10 GHz are 263.2 mm, 278.5 mm and 298.2 mm, respectively, which are 7.02 times, 8.36 times and 9.98 times the corresponding wavelengths, indicating that a larger focal depth off-focus meta-lens is achieved. This kind of off-axis meta-lens has a simple structure, good off-axis focus ability and large focal depth, which has potential applications in a compact and planar off-axis optical system and large focal depth imaging system. Although the working waveband in this article is the microwave band, according to the size scaling effect of the metasurface, it is also possible to design a large focal depth off-axis meta-lens in other bands such as visible light and terahertz bands by using the same method.

Keywords:

Authors and contacts

1.
Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan 430074, China
2.
Wuhan Maritime Communication Research Institute Wuhan 430200, China

Corresponding author: Huang Li-Rong, lrhuang@mail.hust.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61675074)

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References

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Cited By

图 1 (a)基于超表面的波束偏转器; (b)常规的共轴超透镜; (c)离轴超透镜

Figure 1. (a) Beam deflector based on metasurface; (b) conventional on-axis meta-lens; (c) off-axis meta-lens.

DownLoad: Full-Size Img PowerPoint

图 2 (a)离轴超透镜的天线单元; (b)当频率为9 GHz的x偏振波垂直入射到天线单元时, 正交偏振波的透射率和透射相位随l_x的变化关系; (c)满足(3)式的相位分布

Figure 2. (a) Antenna unit of the off-axis meta-lens; (b) when an x-polarized wave with frequency of 9 GHz is incident perpendicularly onto the antenna units, transmittance and transmission phase of the orthogonal polarized wave vary with l_x; (c) phase distributions satisfying Eq. (3).

DownLoad: Full-Size Img PowerPoint

图 3 (a)制备的超表面样品的正面结构照片, 矩形红色虚线为局部放大图; (b)实验装置

Figure 3. (a) Image of the fabricated metasurface sample, and the rectangular red dotted line is a zoom view; (b) experimental set-up.

DownLoad: Full-Size Img PowerPoint

图 4 测试得到的不同频率处正交偏振波的电场强度分布　(a) 8 GHz; (b) 9 GHz; (c) 10 GHz. 红色点划线代表聚焦平面所在的位置, 倾斜的白色虚线代表u₁轴、u₂轴和u₃轴

Figure 4. Measured electric field intensity distributions of the orthogonal polarized waves at different frequencies: (a) 8 GHz; (b) 9 GHz; (c) 10 GHz. The red dotted lines represent the position of the focal planes, and the white dashed lines represent the u₁ axis, u₂ axis and u₃ axis.

DownLoad: Full-Size Img PowerPoint

图 5 工作频率9 GHz处, 透镜焦点处归一化电场强度分布　(a)仿真结果; (b)实验结果

Figure 5. At the working frequency of 9 GHz, the normalized electric field intensity distribution at the focal point of the metalens: (a) Simulation result; (b) experimental result.

DownLoad: Full-Size Img PowerPoint

图 6 测试得到的不同频率处的焦深　(a) 8 GHz; (b) 9 GHz; (c) 10 GHz

Figure 6. Depth of focus at different frequencies: (a) 8 GHz; (b) 9 GHz; (c) 10 GHz.

DownLoad: Full-Size Img PowerPoint

表 1 离轴超透镜的仿真结果和实验结果比较

Table 1. Simulation and experimental results of the off-axis metalens.

入射波频
率/GHz 仿真结果实验结果
α/(°) F₀/mm DOF/mm α/(°) F₀/mm DOF/mm

8 33.2 302.5 223.6 30.5 278.9 263.2
9 30.0 350.0 241.9 27.5 335.4 278.5
10 26.8 385.3 254.3 23.6 400.2 298.2

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map

[1]	Yu N F, Capasso F 2014 Nat. Mater. 13 139 Google Scholar
[2]	Sun S L, H Q, Hao J M, Xiao S Y, Zhou L 2019 Adv. Opt. Photonics 11 380 Google Scholar
[3]	Bi Y, Huang L L, Li X W, Wang Y T 2021 Front. Optoelectron 14 154
[4]	Wan Lei Pan D P, Feng T H, Liu W P, Potapov A A 2021 Front. Optoelectron. 14 1 Google Scholar
[5]	Scheuer J 2017 Nanophotonics 6 137 Google Scholar
[6]	Chen S Q, Li Z C, Liu W W, Cheng H, Tian J G 2019 Adv. Mater. 31 16
[7]	Liu T J, Huang L R, Hong W, Ling Y H, Luan J, Sun Y L, Sun W H 2017 Opt. Express 25 16332 Google Scholar
[8]	Ding J F, Huang L R, Liu W B, Ling Y H, Wu W, Li H H 2020 Opt. Express 28 32721 Google Scholar
[9]	Pan W, Wang X Y, Chen Q, Ren X Y, Ma Y 2020 Front. Optoelectron. 16 6
[10]	Ji C, Song J K, Huang C, Wu X Y, Luo X G 2019 Opt. Express 27 34 Google Scholar
[11]	Ling Y H, Huang L R, Hong W, Liu T J, Luan J, Liu W B, Wang Z Y 2017 Opt. Express 25 29812 Google Scholar
[12]	Khorasaninejad M, Zhu A Y, Roques-Carmes C, Chen W T, Oh J, Mishra I, Devlin R C, Capasso F 2016 Nano Lett. 16 7229 Google Scholar
[13]	Zhuang Z P, Chen R, Fan Z B, Pang X N, Dong J W 2019 Nanophotonics 8 1279 Google Scholar
[14]	Chen W T, Zhu A Y, Sisler J, Bharwani Z, Capasso F 2019 Nat. Commun. 10 1 Google Scholar
[15]	Wang S M, Wu P C, Su V C, Lai Y C, Chu C H, Chen J W, Lu S H, Chen L, Xu B B, Kuan C H, Li T, Zhu S, Tsai D P 2017 Nat. Commun. 8 187 Google Scholar
[16]	Fan Z B, Qiu H Y, Zhang H L, Pang X N, Zhou L D, Liu L, Ren H, Wang Q H, Dong J W 2019 Light Sci. Appl. 8 67 Google Scholar
[17]	Groever B, Chen W T, Capasso F 2017 Nano Lett. 17 4902 Google Scholar
[18]	Chen Q M, Li Y, Han Y H, Deng D, Yang D H, Zhang Y, Liu Y, Gao J M 2018 Appl. Opt. 57 7891 Google Scholar
[19]	Paniagua-Dominguez R, Yu Y F, Khaidarow E, Choi S, Leong V, R, Bakker M, Liang X N, Fu Y H, Valuckas V, Krivitsky L A, Kuznetsov A I 2018 Nano Lett. 18 2124 Google Scholar
[20]	范庆斌, 徐挺 2017 66 144208 Google Scholar Fan Q B, Xu T 2017 Acta Phys. Sin. 66 144208 Google Scholar
[21]	杨皓明 2008 博士学位论文(天津: 南开大学) Yang H M 2008 Ph. D. Dissertation (Tianjin: Nankai University) (in Chinese)
[22]	Khorasaninejad M, Chen W T, Oh J, Capasso F 2016 Nano Lett. 16 3732 Google Scholar
[23]	Zhu A Y, Chen W T, Khorasaninejad M, Oh J, Zaidi A, Mishra I, Devlin R C, Capasso F 2017 APL Photonics 2 036103 Google Scholar
[24]	Zhou Y, Chen R, Ma Y G 2017 Opt. Lett. 42 4716 Google Scholar
[25]	Zhu A Y, Chen W T, Sisler J, Yousef K M A, Lee E, Huang Y W, Qiu C W, Capasso F 2019 Adv. Opt. Mater. 7 1801144 Google Scholar
[26]	Ou K, Li G H, Li T X, Yang H, Yu F L, Chen J, Zhao Z Y, Cao G T, Chen X S, Lu W 2018 Nanoscale 10 19154 Google Scholar
[27]	Zhao H, Quan B G, Wang X K, Gu C Z, Li J J, Zhang Y 2018 ACS Photonics 5 5
[28]	Chen W T, Khhorasaninejad M, Zhu A Y, Oh J, Devlin R C, Zaidi A, Capasso F 2017 Light Sci. Appl. 6 e16259 Google Scholar
[29]	Chen C, Song W, Chen J W, Wang J H, Chen Y H, Xu B B, Chen M K, Li H M, Fang B, Chen J, Kuo H Y, Wang S M, Tsai D P, Zhu S, Li T 2019 Light Sci. Appl. 8 99 Google Scholar
[30]	Zhou Y, Chen R, Ma Y G 2018 Appl. Sci. 8 3
[31]	Banerji S, Meem M, Majumder A, Vasquez F G, Sensale-Rodriguez B, Menon R 2019 Optica 6 6

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